The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation

The newly developed simulation method known as Stokesian dynamics is used to investigate the rheological behaviour of concentrated suspensions. Both the detailed microstructure (e.g. pair-distribution function) and the macroscopic properties are determined for a suspension of identical rigid spherical particles in a simple shear flow. The suspended particles interact through both hydrodynamic and non-hydrodynamic forces. For suspensions with purely hydrodynamic forces, the increase in the suspension viscosity with volume fraction ϕ is shown to be caused by particle clustering. The cluster formation results from the lubrication forces, and the simulations of a monolayer of spheres show a scaling law for the cluster size: l c ∼ [1 − (ϕ/ϕ m ) ½ ] −1 , where ϕ m is the maximum volume fraction that can shear homogeneously. The simulation results suggest that the suspension viscosity becomes infinite at the percolation-like threshold ϕ m owing to the formation of an infinite cluster. The predicted simulation viscosities are in very good agreement with experiment. A suspension with short-range repulsive interparticle forces is also studied, and is seen to have a non-Newtonian rheology. Normal-stress differences arise owing to the anisotropic local structure created by the interparticle forces. The repulsive forces also reduce particle clustering, and as a result the suspension is shear-thickening.

[1]  David J. Jeffrey,et al.  The Rheological Properties of Suspensions of Rigid Particles , 1976 .

[2]  G. Batchelor,et al.  The hydrodynamic interaction of two small freely-moving spheres in a linear flow field , 1972, Journal of Fluid Mechanics.

[3]  M. Fixman,et al.  Viscosity of Polymer Solutions , 1963 .

[4]  R. Pätzold Die Abhängigkeit des Fließverhaltens konzentrierter Kugelsuspensionen von der Strömungsform: Ein Vergleich der Viskosität in Scher- und Dehnströmungen , 1980 .

[5]  Andreas Acrivos,et al.  Shear‐Induced Structure in a Concentrated Suspension of Solid Spheres , 1980 .

[6]  I. Krieger,et al.  Rheology of monodisperse latices , 1972 .

[7]  P. Mazur,et al.  Many-sphere hydrodynamic interactions and mobilities in a suspension , 1982 .

[8]  P. Mazur,et al.  Self-diffusion of spheres in a concentrated suspension , 1983 .

[9]  John F. Brady,et al.  Dynamic simulation of sheared suspensions. I. General method , 1984 .

[10]  W. Russel Bulk stresses due to deformation of the electrical double layer around a charged sphere , 1978, Journal of Fluid Mechanics.

[11]  R. Hoffman Discontinuous and Dilatant Viscosity Behavior in Concentrated Suspensions. I. Observation of a Flow Instability , 1972 .

[12]  W. Russel Review of the Role of Colloidal Forces in the Rheology of Suspensions , 1980 .

[13]  R. Bagnold Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear , 1954, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[14]  Howard Brenner,et al.  Rheology of a dilute suspension of axisymmetric Brownian particles , 1974 .

[15]  C. Beenakker The effective viscosity of a concentrated suspension of spheres (and its relation to diffusion) , 1984 .

[16]  Joseph B. Keller,et al.  Effective viscosity of a periodic suspension , 1984, Journal of Fluid Mechanics.

[17]  A. Acrivos,et al.  On the viscosity of a concentrated suspension of solid spheres , 1967 .

[18]  Denis J. Evans,et al.  The frequency dependent shear viscosity of methane , 1979 .

[19]  G. Batchelor The effect of Brownian motion on the bulk stress in a suspension of spherical particles , 1977, Journal of Fluid Mechanics.

[20]  David J. Jeffrey,et al.  Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow , 1984, Journal of Fluid Mechanics.

[21]  G. Batchelor,et al.  The stress system in a suspension of force-free particles , 1970, Journal of Fluid Mechanics.

[22]  G. Batchelor,et al.  Transport Properties of Two-Phase Materials with Random Structure , 1974 .

[23]  E. Verwey,et al.  Theory of the stability of lyophobic colloids. , 1955, The Journal of physical and colloid chemistry.

[24]  R. Blanc,et al.  Experiments on 2-D suspensions , 1982 .

[25]  R. W. O'Brien,et al.  A method for the calculation of the effective transport properties of suspensions of interacting particles , 1979, Journal of Fluid Mechanics.

[26]  G. Batchelor,et al.  The determination of the bulk stress in a suspension of spherical particles to order c2 , 1972, Journal of Fluid Mechanics.

[27]  S. G. Mason,et al.  The kinetics of flowing dispersions: VIII. Doublets of rigid spheres (theoretical) , 1977 .